Are assets fungible? Testing the behavioral theory …...Are assets fungible? Testing the behavioral...

Are assets fungible?

Testing the behavioral theory of life-cycle savings

Laurence Levin*

Cornerstone Research Suite 250, 1000 El Camino Real, Menlo Park, CA 94025, USA

Received 7 February 1994; received in revised form 14 January 1998; accepted 11 February 1998

Abstract

This paper is an empirical investigation of the behavioral life-cycle savings model. This model

posits that self-control problems causes individuals to depart substantially from rational behavior. I

show that this model can explain how the consumption of individuals at or near retirement vary with

changes in different types of financial assets. Specifically, consumption spending is sensitive to

changes in income and in liquid assets, but not very sensitive to changes in the value of other types

of assets such as houses and social security (even though the value of non-liquid assets is relatively

large for most of the households in the sample). In general, the evidence presented here favors the

Behavioral Life-Cycle Model over the conventional life-cycle model even when liquidity

constraints are introduced. # 1998 Elsevier Science B.V. All rights reserved

JEL classi®cation: D91: Intertemporal consumer choice; Life-cycle models and savings; E21: Consumption;

Savings

Keywords: Savings; Life-cycle; Behavioral models

1. Introduction

According to the simplest versions of the life-cycle theory, a person's consumption

should depend only on the present value of his wealth. This theory has many implications,

the most studied being that individuals should engage in consumption smoothing.

However, this implication has been rejected by most empirical studies.1 Often the failure

Journal of Economic Behavior & Organization

Vol. 36 (1998) 59±83

* Corresponding author. Tel.: +1 415 239 8224; e-mail: [email protected] For e.g., see papers by Flavin (1981), Mankiw (1981), Hall and Mishkin (1982), Hansen and Singleton

(1983), Courant et al. (1986), Carroll and Summers (1989) and Campbell and Mankiw (1989). An excellentsummary of empirical work on the life-cycle hypothesis can be found in Thaler (1990).

0167-2681/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved

PII S 0 1 6 7 - 2 6 8 1 ( 9 8 ) 0 0 0 7 0 - 5

of the life-cycle model is attributed to the presence of liquidity constraints for significant

subsets of the population (see Hayashi (1985) or Zeldes (1989) for examples). This paper

examines whether these anomalous results can be better explained by an alternative

model of savings behavior that takes into account the problem of self-control. This model

is called the behavioral life-cycle model, which was formulated by Shefrin and Thaler

(1988).2

To compare these two models, I examine how consumption varies with both the level

of wealth and the form that wealth takes. In the simplest life-cycle models, consumption

should only depend on an individual's total wealth, in other words, assets should be

fungible; receiving $ 100 today should have as much effect on an individual's spending as

receiving $ 100�interest next year, or a $ 100 appreciation of the value of his house.3 The

behavioral life-cycle model predicts that assets should not be fungible, implying that an

individual's consumption decisions will be affected by asset composition as well as total

wealth.

The behavioral life-cycle model as developed by Shefrin and Thaler is a simple model

of self-control based on three ideas. First, individuals are tempted to spend all their

resources on current consumption instead of saving for the future. Second, individuals

who save, overcome this self-control problem by investing in a variety of assets that have

different levels of temptation associated with them. A historic example of this type of

asset was Christmas clubs which were savings plans (usually with low or non-existent

interest rates) that did not allow withdrawal unto December. Individuals invested in them

to insure they had enough money saved for Christmas presents. Thus, individuals create

mental accounts for their different assets causing their marginal propensities to consume

from those assets to vary with the level of temptation associated with each one. Third,

setting up these mental accounts implies that individuals engage in `framing'; a person's

consumption spending not only depends on total wealth but also depends on how that

wealth is allocated among assets with differing levels of `temptation.' For example,

individuals are more willing to spend assets they have labeled current income than those

they have labeled wealth or those that they expect in the future. Essentially, the

behavioral life-cycle posits that there are psychological as well as financial transaction

costs associated with spending from different types of assets.

This paper contains the first formal empirical tests of the behavioral life-cycle model

using a large panel dataset such as those that have been used to study other models of

savings. Previous evidence for the behavioral life-cycle (collected in Thaler, 1992) has

either come from small surveys of college or MBA students or been garnered from

anomalies found in other studies that were not designed to test the behavioral life-cycle

model. Although this type of evidence is valuable, it cannot be definitive because of small

sample size or possible biases in studies that were not designed to study behavioral

decision making. Testing the behavioral life-cycle model necessitates taking the

assertions of that model and creating empirical tests that distinguish between it and

2 This theory can be interpreted as a formalization of an older literature which had rejected some of theimplications of permanent income/life-cycle models but found that wealth was still an important element inmaking consumption decisions. This literature is summarized in Mayer (1972).

3 Liquidity constraints and other extensions of the life-cycle model may also cause fungibility to be rejected.See the discussion in Section 2.

60 L. Levin / J. of Economic Behavior & Org. 36 (1998) 59±83

conventional models of life-cycle savings. It also requires building an econometric model

that controls for the biases inherent in examining consumption data.

Another novel feature of this paper is that many goods are used to study consumption.

In previous empirical studies of consumption only food spending is used because it is the

only category of consumption included in the PSID and other commonly used datasets. In

this paper, I use the Retirement History Survey which contains information on how much

is spent on ten different goods. This creates an opportunity to investigate how spending

patterns differ between goods.

In the next section, I derive four testable differences between the behavioral and

conventional life-cycle models. The first two tests are straightforward comparisons of the

marginal propensity to consume (MPC) out of different types of assets. The third test

examines whether liquidity constraints are causing the observed differences in assets'

MPC and is derived from differences between the two models on the effect of liquidity

constraints. Essentially this test examines whether liquidity constraints occur because of

an inability to liquify certain assets or because of large psychological or financial

transaction costs in doing so. The final test is an examination of whether transaction costs

seem to be financial or psychological in nature. This test is derived by looking for

evidence of framing in consumption. For a conventional life-cycle model individual, the

propensity to consume a particular good out of any asset will depend only on the good's

wealth elasticity and possible financial transaction costs. However, if an individual acts

according to the behavioral life-cycle model, then the form wealth takes affects the type

of wealth the individual consumes. In other words, the psychological cost of using an

asset to finance the consumption of a particular good is a function of that good's

attributes. In this case the propensity to consume a particular good out of a particular

asset will depend on the attributes of both the good and the asset.4

In Section 3, the data and the statistical methods are discussed. Section 4 contains the

empirical results, and Section 5 is the conclusion.

The results of this paper provide strong evidence against assets being fungible. For

many individuals consumption does not seem to be very sensitive to changes in their

wealth portfolios. Further, assets' marginal propensities to consume are very different and

show strong evidence in favor of the presence of large transaction costs. Finally, the

behavior of liquidity constrained individuals is consistent with the expected effects from

framing. In general then, this paper finds strong evidence in favor of the behavioral life-

cycle model in comparison to the conventional life-cycle model.

2. Modelling consumption expenditures

2.1. Framework

In this section a simple framework is introduced in order to formalize tests of the

differences between the behavioral and conventional life-cycle models. To establish the

4 Although this implication of the behavioral life-cycle theory is not explicitly discussed by Shefrin and Thaler(1988), Shefrin and Thaler have derived this result in an unpublished mimeo, Shefrin and Thaler (1981).

L. Levin / J. of Economic Behavior & Org. 36 (1998) 59±83 61

framework, compare the expenditure function of a conventional life-cycle individual (EL)

to one who acts in a behavioral manner (EB), both with income (Y) and K different types

of assets (A1-AK).

In the simplest model, a conventional life-cycle individual's expenditures will only be a

function of his total resources. The individual's total resources (W) are the sum of his

assets plus the capitalized value of his permanent income which can be written as �Y

where � is

� �XT

t�1

1 � Pt

�1� r�t (1)

where Pt�survival probability, r�interest rate, T�time horizon.

Thus the total resources of an individual are: W � �Y ��Ai. Therefore, the

conventional life-cycle individual's expenditure function for the gth good can be written

as

ELg � ELg�W� � ELg �Y �XK

k�1

Ak

!(2)

For a behavioral life-cycle individual, consumption will depend not only on his total

resources but also on how those resources are split up between different types of assets.

Thus the expenditure function for a behavioral life-cycle individual will be

EBg � EBg�Y ;A1;A2; . . . ;Ak� (3)

In this case, there is no single aggregate that an individual uses when making an

expenditure decision. From these expenditure functions one can easily derive the

marginal propensity to consume (MPC) out of a given asset. For a conventional life-cycle

saver the marginal propensity to consume out of any asset (i or j) is

@ELg

@Ai

� @ELg

@Aj

� @ELg

@Wand

@ELg

@Y� � @ELg

@W(4)

For income this formulation assumes that income is permanent income. If changes

in income were completely transitory then the MPC of income would equal the MPC

of wealth. Thus, the value of the MPC from an addition to income relative to the

MPC from an addition to wealth will range between the MPC of wealth (if the income

change is transitory) and (if the income change is permanent) and will depend on

how permanent the change in income is. Note that the MPC from income will never be

greater than a! For a behavioral saver the marginal propensity to consume out of an asset

will be

@EBg

@Ai

>@EBg

@Aj

> � � � > @EBg

@AK

and@EBg

@Y> �

@EBg

A1

(5)

where the assets are arranged in descending orders of temptation or liquidity (A1 is more

tempting than A2 etc.); further, even if Y is transitory, its high temptation level will cause

its MPC to be higher then the MPC of an equivalent change in wealth.


2.2. Test 1 (Comparing the MPC from income to the MPC from wealth)

The first test derives from comparing Eq. (4) to Eq. (5). This test consists of examining

the sensitivity of consumption to income relative to wealth. According to behavioral life-

cycle theory, spending should be very sensitive to income and much less sensitive to

wealth. Thus if the behavioral theory is right, a regression of consumption against income

and other assets should find that income is usually significantly related to consumption,

while other assets may not be. Further, if the conventional theory holds, the ratio of the

MPC of permanent income to the MPC of wealth should equal, the capitalized value of a

$ 1 worth of permanent income; if the behavioral theory is correct this ratio will be larger

than.

2.3. Test 2 (Testing for the equality of different assets' MPC)

The second test also directly follows from the framework developed above. This test

compares the MPCs of different assets. If individuals are conventional life-cycle savers

then the MPCs of the different assets should be equal. In other words assets should be

perfect substitutes. However, if individuals are behavioral life-cycle savers then the MPC

of different assets will not be the same and should, instead, be a function of the level of

temptation associated with the particular asset. Thus, this test consists of examining

whether or not the MPCs are equal.

2.4. Test 3 (Testing for liquidity constraints)

Obviously there are explanations other than the behavioral life-cycle hypothesis that

predict Tests 1 and 2 would fail. The addition of liquidity constraints to the simplest

convention would, by themselves, cause assets to not be fungible. If individuals cannot

borrow against some of their assets then even the conventional life-cycle model will

predict that less liquid assets will have lower marginal propensities to consume. The third

test compares the MPC of different asset types for constrained and unconstrained

individuals. The idea behind this test is that in a conventional life-cycle model liquidity

constraints are externally imposed by market imperfections which limit the ability to

borrow against future income whereas in the behavioral life-cycle model, liquidity

constraints may also be internally imposed by the consumer. The testable difference

between internal and external liquidity constraints is that if the constraint is external, the

value of an illiquid asset will affect consumption as long as other more liquid assets

are still being held (since an increase in this asset just adds to general wealth) but will

cease to affect consumption when those more liquid assets are depleted, since then the

liquidity constraint will be binding. The opposite result holds when the liquidity

constraint is internally imposed. As long as more tempting assets have not been

exhausted, the value of the less tempting asset will not affect the decision on how much to

consume. Instead a less tempting asset will be consumed only after more tempting assets

are exhausted.

To formalize this test, assume there are two assets denoted A1 and A2. A1 is a liquid

asset (for example, the value of a checking account) while A2 is an asset that is less


liquid (for example, a house) that will eventually be liquidated. For a conventional

life-cycle individual, the value of A2 will only affect consumption when the liquidity

constraint is not binding. This occurs when the value of A1 is large. If the value of

A1 is small the individual is liquidity constrained causing an increase in A2 to

have no effect on consumption since there is no way the individual can access it. In

our example, if a person who is not liquidity constrained (a lot of money in his

bank account) finds that his house has doubled in price then his consumption

will increase. However, if he is liquidity constrained then the increase in the value

of his house will not change his consumption expenditures because he cannot borrow

against it.

Formally then his consumption expenditures will follow this pattern

@EL

@A2

��A1�0

> 0 and@EL

@A2

��A1�0

� 0 (6)

Two implications of the behavioral life-cycle model predict that the effects of liquidity

constraints will be completely different from those described in Eq. (6). First, as

discussed earlier, the liquidity constraints of a behavioral life-cycle individual are

internally imposed in addition to being externally forced upon him by imperfections in

the capital market. In this case a less liquid or tempting asset (A2) will only affect his

consumption when other more tempting assets (A1) are depleted and he needs to use it.

For example, an increase in the value of a house only affects consumption when another

less tempting asset is exhausted. If there is plenty of liquid wealth available, a change in

the value of the house will not alter the individual's consumption decision because the

value of the house does not enter into his decision making process. However, if the person

is strapped for cash then he will want to dip into those less liquid assets. Since the

constrained individual is (at least implicitly) using those assets, the components of his

decision making process will now include them. In this case, a change in the value of

these assets will affect his consumption pattern. Second, if the behavioral life-cycle

model is true then individuals who adopt the rules of behavior suggested by it will be

more successful at saving than those who do not. In this case the individuals who are least

tempted to use illiquid assets to support consumption will be the individuals with

relatively larger savings. Thus even after controlling for an individual's initial resources

(through a fixed effect or other econometric controls-see below) we will find a differential

response to an exogenous change in a particular asset's value between the group

that looks liquidity constrained and the group that does not. Formally, both these

reasons imply that a behavioral life-cycle individual's consumption will follow this

pattern

@EL

@A2

��A1�0

� 0 and@EL

@A2

��A1�0

> 0 (7)

Thus the conventional life-cycle theory and the behavioral life-cycle theory have

strongly contrasting and testable implications about the effects of liquidity constraints on

consumption behavior.


2.5. Test 4 (Testing for psychological versus financial transaction costs)

Testing for framing in consumption is complicated. Proponents of the conventional

life-cycle hypothesis maintain that differences in various assets' marginal propensities to

consume may result from those assets having differential risk characteristics, or tax rates5

or other features that cause a one dollar increase in the value of a house to have the same

effect on spending as, say a 50 cent increase in some other asset. The most important

objection to Test 3 (see Skinner, 1993) is that the existence of fixed monetary costs of

transforming illiquid assets into consumption may also cause Test 3 to be rejected. Thus

Test 3 is actually a test of whether there are costs to transforming assets but does not test

directly whether those costs are financial or psychological in nature.

However there is a testable difference between the psychological and the financial

theory of liquidity constraints. Note that if the financial explanation of transaction costs is

correct then there still is a single aggregate of resources (W) upon which an individual

bases all his consumption decisions on. In this case how an asset maps into W depends on

its characteristics alone, not the characteristics of the good being consumed. Let �k�Ak�be the function that transforms the value of asset Ak into W. W is now a sum of all the

(transformed) assets and a conventional life-cycle individual's expenditures on a

particular good (g) will be

ELg � ELg�W� � ELg

XK

k�1

�k�Ak� !

(8)

Now suppose we have two different goods (g and h) and two different assets (A1 and

A2). In this case the individual's wealth will be: W � �1�A1� � �2�A2� and his

expenditures on two the goods will be

ELg�W� � ELg��1�A1� � �2�A2�� and ELh�W� � ELh��1�A1� � �2�A2��If we take the derivatives of the expenditure functions of one of the goods (g) with

respect to one of the assets (k) we have

@ELg

@Ak

� @ELg

@W� @W

@Ak

� @ELg

@W� �0k�Ak� (9)

The @ELg=@W is the marginal propensity of a conventional life-cycle individual to

consume a good for a given change in wealth while @W=@Ak � �0k�Ak� is how the change

in a particular asset is transformed into a change in wealth. The marginal propensity to

consume a particular good out of wealth is obviously not going to be equal for different

goods, since its value will depend on the good's wealth elasticity. However, the second

term does not depend on what particular good is chosen since its value just depends on

how the asset is transformed into wealth and should be the same for all goods. If a

conventional life-cycle individual consumes two goods (g and h), then the ratios of the

5 For example, consider a individual with 2 assets, A1 and A2. If A2 is taxed at a rate of the individual's totalresources will be W � A1 � �1ÿ ��A2 and the propensity to consume out of those two assets on a good (G) willbe: @G=@A1 � @G=@W and @G=@A2 � �1ÿ ��@G=@W .


marginal propensities to consume out of the two assets will be equal since

@ELg=@A1

@ELg=@A2

� @ELg=@W � �01�A1�@ELg=@W � �02�A2� �

�01�A1��02�A2� �

@ELh=@A1

@ELh=@A2

(10)

For a behavioral life-cycle individual, however, the relationship between an

expenditure on a certain good and the value of an asset will depend on both the good's

and asset's characteristics. In this case the propensity to consume a particular good out of

a particular asset should depend on the attributes of both the good and the asset. As an

example, compare spending on groceries to spending on vacations. The conventional

model, discussed above, would predict that after controlling for the different wealth

elasticities of the two goods, a change in the value of a home or a business will affect

spending on groceries by as much as it affects spending on vacations. On the other hand,

the behavioral model predicts that spending on a good (like groceries) that is purchased in

small quantities every day will be less influenced by the value of a particular asset then a

good that is purchased infrequently at a higher cost. In other words, the behavioral life-

cycle model predicts that when an individual finds his house has increased in value he

will be more likely to change his vacation plans than his grocery purchases. For a

behavioral life-cycle individual, then, Eq. (10) will not hold; the ratios of the MPCs

between assets and spending on different goods given in Eq. (10) will no longer be equal.

Thus Eq. (10) suggests a very general test between the two competing hypotheses. If

people engage in framing then asset composition will affect both the composition of

spending as well as its size.

3. Data and statistical methods used in the study

3.1. Data

The data used in this study is from the Longitudinal Retirement History Survey (RHS).

This survey interviewed around 11 000 household heads who were between 57 and 62 in

1969. This survey was repeated every 2 years until 1979, creating six waves. The survey

contains detailed information on family status, wealth, social security, income and

expenditures.

The RHS has several features that makes it useful in studying the effect of wealth and

income on consumption. First, creating a value for future wealth is much simpler for a

group near retirement than for a group of younger cohorts. Determining the value of

future wealth of a relatively young person is extremely difficult since it will depend on his

future wage income as well as his future social security and pension, all of which are

extremely difficult to predict. On the other hand, since the individuals in the RHS are

either retired or near retirement, their social security wealth and pension wealth are

known or can be predicted with a much larger degree of certainty. Further, future wage

income is a much lower portion of future wealth for the elderly, making exact modelling

relatively less important. The second advantage of using a sample of the elderly is that

liquidity constraints are relatively unimportant for them. The inability to borrow against

future labor income may cause younger individuals to be seriously liquidity constrained.


However, the peak earning years of the elderly are behind them. Thus their spending

patterns should not be as constrained by their inability to borrow against future income. A

third advantage of the RHS is that it is a relatively long panel (10 years), during which

most of the households progress from one stage of the life-cycle (working) to another

(retirement). Thus we may be able to examine how life-cycle changes affect the

relationship between consumption spending and asset type.

To study consumption, I use eight of the ten expenditure categories6 in the RHS as

dependent variables. All expenditure categories are annual expenditures for an entire

household. The eight consumption variables are listed below. Unfortunately, not all the

consumption questions were asked for all of the waves of the RHS; the dependent

variables and their range are listed below:

Dependent Variable In 1969 In 1971 In 1973 In 1975 In 1977 In 1977

Food Eaten at Home

(Groceries)

Yes Yes Yes Yes Yes Yes

Food Eaten Out (Food Out) No* Yes Yes No* Yes Yes

Charitable Contributions Yes No No Yes Yes Yes

Dues to Clubs Yes Yes No Yes Yes Yes

Entertainment Yes Yes No Yes Yes Yes

Gifts Yes Yes No Yes Yes Yes

Transportation No Yes Yes Yes Yes Yes

Vacations Yes Yes Yes Yes Yes Yes

* For Food Out, 1969 and 1975 were excluded because the values for those 2 years

were not consistent with the values for the other years.

Unfortunately this data cannot be combined into one total consumption category

because of missing values. Since there are relatively few observations which have non-

zero values for all eight categories, a different equation for each consumption category

will be estimated.7

Two sets of independent variables are used in this study. The first set is household

characteristics. Since the equations are estimated using fixed effects (see ahead), only

household characteristics that change over time need to be controlled for. The included

characteristic variables are married dummy (Married), retirement dummy (Retire), spouse

employment dummy (Spouse Work), changes in health status (Feel Better-Health better

than 2 years ago, Feel Worse-Health worse than 2 years ago) and number of people in the

household (#_in_House). The Retirement dummy was constructed in two steps. First,

those who said they were retired and had wage incomes of less than $ 1000 a year were

6 The two missing categories are amounts spent on chores and amounts spent on non-vacation trips. Very fewhouseholds have more than one non-zero observation for either of these categories. Therefore these categoriescould not be analyzed in the manner discussed in Section 3.3.

7 I have also excluded single women who were never married during the panel (the RHS does not contain menwho were single in 1969). Preliminary investigation has shown that their reported consumption behavior is muchdifferent from the behavior of couples and is not explained by changes in their income or any other variable.This may be due to less accurate data (we do not have social security records for their husbands) and otherwealth data may be incorrect. Although including these women does not substantially change the results, it doesweaken them.


considered retired. Second, for individuals who did not respond to the retirement question

or claimed they were not retired, the retirement dummy was constructed by finding the

first year that their wage earnings were less than $ 1000 and then stayed less than that in

subsequent waves. Using this definition, most individuals were retired by 1977 and all

were retired by 1979.

The second set of independent variables consists of the different assets. In this study, I

use five types of assets: current income, liquid assets, value of house, future assets and

non-liquid assets. Current income (Income) consists of wages, net interest income,

dividends, social security, pension income, and business or farm income less payments on

debts. Liquid assets (Liquid Wealth) consist of assets that are relatively easy to transform

into cash. These include checking and savings accounts, stocks and bonds, and

(negatively) the value of any non-secured debt. House value (House) is the net equity in

the home (market value of home less the mortgage). Future assets (Future Wealth)

include the (actuarially discounted) present value of social security and pension income

plus the discounted value of future labor income.8 Non-liquid assets (Property) consist of

everything that remains, including net value of farm, business, and other (non-house)

property. All asset values are net of current payments to the household (which are counted

as income).

In many studies of consumption, rejection of life-cycle models is attributed to liquidity

constraints caused by an inability to borrow against future labor income (for e.g., see

Zeldes, 1989 or Deaton, 1989). Although most of the individuals in this study are near

retirement, some might still wish to borrow against future social security or pension

income and find themselves unable to. To examine whether this is important I have split

the sample into constrained and unconstrained subsamples in a manner analogous to

Zeldes. I have defined the unconstrained group as those households whose liquid wealth

exceeds at least 3 months of household income for at least five of the six periods in the

sample, while the constrained group consists of everyone else.

3.2. Means

Table 1 contains the means of the consumption and asset variables used in the different

regressions (which are labelled at the top).9 Since each regression is taken from a

different sample, the means of the variables in each of the regression samples are

reported. The first row (labelled consumption) is the mean of the dependent variable used

in that regression. The means are for the entire sample and are also broken down for the

constrained and unconstrained subsamples.

One striking result from the table of means is that the households who are in the

Entertainment, Vacation, and Dues regressions have a higher mean for income and wealth

then the households in the other spending categories. Mean Income for these three

8 I assumed that individuals have perfect foresight about their future career path (i.e. know both their futureincome and when they will retire) and so use their actual earnings to calculate their expected future income. Itturns out that including or not including future labor income does not change the results very much, so a moresophisticated treatment of future income is probably not worthwhile (almost two-thirds of the sample wereretired by the third wave).

9 Means of the household characteristic variables are available upon request.


Tab

le1

Mea

ns

and

num

ber

of

ob

serv

atio

ns

for

the

wea

lth

and

consu

mpti

on

var

iable

s

Gro

up

Gro

ceri

esF

ood

out

Char

ity

Dues

Ente

rtai

nm

ent

Gif

tsT

ransp

ort

Vac

atio

nA

lla

Dep

end

ent

var

iab

le*

Over

all

$1

14

6$

691

$171

$62

$111

$165

$307

$635

$3287

Un

con

stra

ined

$1

11

7$

723

$194

$68

$115

$183

$314

$677

$3393

Con

stra

ined

$1

19

1$

639

$125

$44

$92

$128

$293

$418

$2930

#o

fo

bse

rvat

ion

sO

ver

all

25

05

2211

2432

835

520

2356

909

594

Un

con

stra

ined

15

48

1360

1598

608

428

1570

597

498

Con

stra

ined

95

7851

834

227

92

786

312

96

Inco

me

Over

all

$8

60

2$

5514

$5826

$9393

$11

127

$7463

$7665

$12

493

Un

con

stra

ined

$9

75

2$

6294

$6497

$10

075

$11

453

$8190

$8553

$12

934

Con

stra

ined

$6

74

0$

4268

$4539

$7565

$9609

$6012

$5964

$10

203

Liq

uid

wea

lth

Over

all

$1

34

83

$9104

$10

953

$19

891

$24

603

$12

420

$13

772

$26

201

Un

con

stra

ined

$2

06

81

$14

028

$15

680

$26

309

$28

899

$17

553

$19

923

$30

332

Con

stra

ined

$1

83

8$

1234

$1896

$2702

$4618

$2167

$2001

$4771

Fu

ture

wea

lth

Over

all

$3

99

23

$27

216

$25

565

$38

301

$42

151

$33

527

$37

297

$50

459

Un

con

stra

ined

$4

31

03

$29

627

$27307

$39600

$42

933

$35

502

$40

213

$51

045

Con

stra

ined

$3

47

79

$23

362

$22

227

$34

824

$38

514

$29

581

$31

718

$47

416

Pro

per

tyO

ver

all

$1

41

89

$8952

$9516

$17

565

$19

159

$11

726

$11

765

$21

855

Un

con

stra

ined

$1

78

38

$11

271

$11

280

$20

146

$20

567

$13

739

$14

426

$23

298

Con

stra

ined

$8

28

6$

5246

$6137

$10

650

$12

605

$7706

$6674

$14

370

Ho

me

val

ue

Over

all

$2

02

54

$13

868

$14

694

$20

654

$22

159

$17

689

$17

796

$24

783

Un

con

stra

ined

$2

31

80

$15

712

$16

165

$21

883

$23

378

$19

445

$20

084

$25

748

Con

stra

ined

$1

55

20

$10

923

$11

877

$17

362

$16

487

$14

182

$13

417

$19

777

Th

eto

pro

win

each

bo

xis

the

mea

nfo

rth

een

tire

sam

ple

.T

he

row

titl

ed`C

onst

rain

ed'

con

tain

sm

eans

for

the

subsa

mple

whose

liquid

wea

lth

isle

ssth

an6

month

sof

inco

me.

Th

ero

wti

tled

`Unco

nst

rain

ed'

con

tain

sm

eans

for

the

subsa

mple

whose

liquid

wea

lth

isgre

ater

than

6m

onth

sof

inco

me.

*M

ean

so

fD

epen

den

tan

dIn

dep

enden

tV

aria

ble

su

sed

inre

gre

ssio

nfo

rth

atco

nsu

mpti

on

cate

gory

.a

All

isth

esu

mo

fth

em

ean

so

fth

eco

nsu

mp

tio

nca

tegori

es.


samples is over $ 10 000 while for the other five categories mean income is near $ 8000.

A similar result holds for the various wealth variables. The reason for this is that there are

fewer observations for these categories than there are for the other ones, and being in this

sample is positively correlated with wealth. Although it is obvious why taking vacations

correlates strongly with wealth it is somewhat odd that joining a social club (which has an

average expenditure of only $ 69) or spending on entertainment should be. This

heterogeneity in the samples should be remembered when comparing the results from the

eight regressions. Further, even though the combined results will be reported they can

only be interpreted as indicative, not definitive.

Another less surprising result is that the constrained group is on average poorer than

the unconstrained group. For example, the constrained group's mean income is around 25

percent lower than the unconstrained group's mean income. Even more striking, the

constrained group's mean liquid wealth is only 10±15 percent of the unconstrained

group's mean liquid wealth. The other wealth variables are also considerably lower for

the constrained group then for the unconstrained group.

The column marked ALL contains the sum of the means of the eight consumption

variables. The value of $ 3287 is the sum of the eight categories mean spending levels and

is between 25±40 percent of income. This provides good evidence that the eight

consumption variables are a large proportion of total consumption spending.

3.3. Empirical methods

To consistently estimate different assets' MPCs, five major econometric problems need

to be solved. These problems are: Unobserved differences between individuals,

autocorrelation of errors between years, measurement error in the wealth data, possible

simultaneity bias between spending and savings decisions, and sample selection bias

caused by missing observations. Any consistent estimator of the effect of asset

composition on consumption must take these problems into account.

Unobserved differences between individuals may result in people with the same level

of income having different amounts of savings. These differences may be caused by

different tastes for savings, different income paths (individuals whose income is more

variable may have more precautionary savings), or differences in luck. The coefficients

from a standard regression of assets on consumption may be contaminated by these

unobserved differences. This bias occurs because the estimated coefficient of a particular

asset will include both the marginal propensity to consume from that asset and the cross-

correlation between the unobservable differences, the value of the asset and consumption.

To solve this problem, I will use fixed effects. Fixed effects sweep out the unobserved

differences between people by subtracting out the individual means from all the variables

before estimation.10 This method is equivalent to using individual dummy terms in all the

equations. This technique should eliminate the contamination caused by the unobserved

10 This method is somewhat unorthodox. Griliches and Hausman (1986) suggest sweeping out the means byfirst differencing and using a slightly different set of instruments. Since some of the dependent variables aremissing in the middle of the sample (usually 1973) first differencing would lead to some excess data loss.Preliminary investigations using first differences on grocery and vacation spending (which span all 6 years)suggest that the results of the Griliches-Hausmann technique and those reported here are very similar.


differences and allow for unbiased estimates of the MPCs. Even though this technique

allows the estimates to be conditioned on the individual's initial resources, it does not

control for differential responses of these individuals to exogenous changes in the value

of those assets. In this case the estimated parameter can be interpreted as the average

MPC of a particular asset for a given sample. If the sample changes then the MPC may

change with it (see discussion in Section 2 on why samples might have different MPCs).

The problem of auto-correlation of the equations' error term can be dealt with

straightforwardly. Instead of assuming that the error term follows an AR(1) or AR(2)

process that is constant between periods, I allow the autocorrelations between the

different years to be free parameters that are estimated directly. The method11 for doing

this is to treat each year as a separate equation. Then the equations for the different years

are estimated jointly by a method similar to seemingly unrelated regressions or three-

stage least squares in which the covariances between equations are actually the auto-

correlations of the error terms and are estimated directly.

A typical problem with using wealth data is that this data is often riddled with

measurement error. The RHS is no exception (see Hurd, 1987). To control for

measurement error, I use a technique devised by Griliches and Hausman (1986), which

utilizes the panel structure of the RHS. Their technique exploits the multiple observations

per individual that panel datasets contain. To instrument a variable contaminated by

measurement error one uses the value of that variable from different periods. For

example, to instrument liquid wealth in the 1975 equation one can use the value of liquid

wealth in 1973 and 1977 as instruments, while to instrument liquid wealth in the 1977

one would use the 1975 and 1979 values. This method is consistent as long as the

measurement error does not follow a moving average (MA) or auto-regressive process but

there is autocorrelation in the true value (since otherwise the variables would not be good

instruments). The assumption of no MA component in the measurement error can be

tested for by calculating a Hausman-Specification test comparing the estimates when the

adjacent time period values are used as instruments with the estimates when the

instruments are drawn from values from periods further away (which would not be

affected by a MA error).12

In a similar manner, simultaneity bias can also be tested for and corrected. A potential

problem for estimating the effect of wealth on consumption is that decisions on how

much to consume and how much to save may be made simultaneously; if you decide to

save more you will consume less. In this case, using the future values of the wealth

variables as instruments will not lead to consistent estimators because a consumption/

savings decision in an earlier period will affect the future values of those variables too.

This effect can also be tested for by calculating a Hausman test statistic comparing the

estimates that use both the future values and past values of the asset values as instruments

(and so should be more efficient if measurement error is the major problem) with the

estimates that only use assets' past values, which are consistent even when simultaneity

11 This method is outlined in Hsiao (1987).12 Testing for autocorrelation in the measurement error is much harder (if not impossible). However, if

autocorrelation of the measurement error was a serious problem then the estimates would still change wheninstruments of different lengths were used, which might be discerned by a Hausman test.


bias occurs because their values are not affected be current decisions (i.e. their values are

predetermined).13 The test statistics for both measurement error and simultaneity bias

will be reported below.

The final problem with the data is sample selection. Many of the observations do not

have complete (or even any) information on the consumption categories for all the

periods, or claim that the value of that good is zero (which seems implausible for some of

the categories, particularly groceries). Although one could handle this problem by

making some strong assumption about the error distribution (such as normality) I will

instead only use households that have valid non-zero consumption values for all the

periods. I am thus assuming that for the households selected by this criteria, the process

that puts them into the sample is constant over the time-span and so is a fixed effect. By

controlling for these fixed effects, I will control for any sample selection effect.

The method outlined above differs from normal three-stage least squares in two ways.

First, the coefficients of the variables are restricted to be the same across all the equations

(which are the years). Second, to use three-stage least squares one must assume that all

the instruments can be used in all of the equations. Since the instruments are the values of

the non-adjacent variables, this method will not work. Instead one must use a generalized

method of moments estimator that allows the instruments to vary between equations.

4. Empirical results

4.1. General regression results

The baseline regression results are in Table 2. Table 3 contains results on the

differences between the estimated MPCs. The estimates of the MPCs for both the

liquidity constrained and non-liquidity constrained subsamples are in Table 4. For all four

tables, columns are labelled with the consumption category that is the dependent variable.

The column labelled All is the aggregate consumption category and is the sum of the

previous eight columns. In this section, I discuss some general results from the

regressions. In the sections following, specific tests between the conventional and

behavioral life-cycle hypotheses developed earlier are conducted.

The first parts of Tables 2 and 4 contain the R2 and the number of observations for the

different regressions. Table 2 also contains the chi-square statistics on tests of various

hypotheses. The second part of Tables 2 and 4 are estimates of the MPCs of the different

assets.

The first part of each table reveals very low values of R2. One reason for this is that by

using a fixed effect one takes out the between variation (in a cross-section regression the

R2 is between 0.3 and 0.4) but retains a lot of the variation caused by measurement error

in the dependent variable. Luckily, even though the R2 is small, some effects can still be

discerned.

13 At a minimum, acceptance of the hypothesis of no simultaneity bias implies that even if there is actuallysome bias, the effect of this bias is small relative to the variance of the estimates.


Tab

le2

Ex

pen

dit

ure

fun

ctio

nre

sult

s±

reg

ress

ion

stat

isti

csan

dw

ealt

hco

effi

cien

tsfo

rth

eco

mbin

edsa

mple

Gro

ceri

esF

ood

out

Char

ity

Dues

Ente

rtai

nm

ent

Gif

tsT

ransp

ort

Vac

atio

nA

lly

R2

0.1

10

.09

0.0

60.0

20.0

10.0

30.0

20.0

1

#o

fo

ber

vati

on

s2

50

52

21

12432

835

520

2356

909

594

Sim

ult

anei

tyte

stc2

13

.96

26

.48

**

8.8

218.9

610.0

615.2

15.8

722.8

6

Mea

sure

men

ter

ror

test

c22

2.6

52

8.0

1**

10.1

711.5

110.6

322.2

616.2

220.7

3

Est

imat

eso

fm

arg

inal

pro

pen

siti

esto

con

sum

e(M

PC

)of

dif

fere

nt

asse

ts

Inco

me

11

.47

**

1.7

88.8

2**

1.0

8**

0.9

4*

6.6

8**

10.7

1**

0.2

441.7

3

(t-s

tati

stic

)(5

.50

)(0

.71)

(7.2

5)

(2.6

2)

(1.7

4)

(7.9

4)

(5.2

6)

(0.1

3)

Liq

uid

wea

lth

ÿ0.0

40

.33

*ÿ0

.06

0.0

8*

0.0

7**

0.4

6**

0.3

3**

0.4

4**

1.6

1

(t-s

tati

stic

)(0

.28

)(1

.90)

(0.6

1)

(2.9

0)

(2.4

0)

(5.4

9)

(3.0

9)

(2.8

7)

Fu

ture

wea

lth

1.6

8**

0.1

20.2

7ÿ0

.11

0.1

00.3

2**

ÿ0.5

9ÿ0

.57

1.2

3

(t-s

tati

stic

)(3

.14

)(0

.18)

(1.1

4)

(1.3

5)

(0.5

9)

(2.0

1)

(1.6

3)

(1.1

8)

Pro

per

ty0

.12

ÿ0.1

7ÿ0

.06

ÿ0.0

5**

0.1

1**

0.0

30.4

5**

0.1

30.5

5

(t-s

tati

stic

)(1

.00

)(0

.73)

(0.7

0)

(2.3

3)

(3.0

7)

(0.4

0)

(4.0

3)

(1.0

5)

Ho

me

val

ue

0.4

7ÿ0

.05

ÿ0.1

8ÿ0

.06

ÿ0.0

4ÿ0

.14

0.2

4ÿ0

.24

0.0

1

(t-s

tati

stic

)(1

.25

)(0

.09)

(1.1

4)

(1.4

6)

(0.5

0)

(0.9

1)

(0.8

5)

(0.8

4)

**

Sig

nif

ican

tat

5p

erce

nt

level

*S

ign

ific

ant

at1

0p

erce

nt

level

.*

yA

llis

the

sum

of

the

inco

me

or

wea

lth

coef

fici

ents

for

all

of

the

consu

mpti

on

cate

gori

es.

Th

ec2

test

sfo

rp

ote

nti

alsi

mu

ltan

eity

or

mea

sure

men

ter

ror

bia

s.S

eete

xt

for

det

ails

.


Tab

le3

Tes

tsfo

rth

eeq

ual

ity

of

dif

fere

nt

wea

lth

coef

fici

ents

MP

Cs

Gro

ceri

esF

ood

Out

Char

ity

Dues

Ente

rtai

nm

ent

Gif

tsT

ransp

ort

Vac

atio

nA

lla

Inco

me±

Liq

uid

wea

lth

11

.51

**

1.4

68.8

8**

1.0

0**

0.8

86.2

1**

10

.39

**

ÿ0.2

040.1

2

(t-s

tati

stic

)(5

.45

)(0

.57)

(7.2

7)

(2.4

0)

(1.6

2)

(7.2

8)

(5.0

4)

(0.1

1)

Inco

me±

Fu

ture

wea

lth

9.7

9**

1.6

68.5

5**

1.1

9**

0.8

56.3

5**

11

.31

**

0.8

140.5

0

(t-s

tati

stic

)(4

.33

)(0

.62)

(6.7

2)

(2.7

3)

(1.4

6)

(7.1

7)

(5.3

1)

(0.4

1)

Inco

me±

Pro

per

ty1

1.3

5**

1.9

68.8

8**

1.1

3**

0.8

36.6

5**

10

.26

**

0.1

241.1

8

(t-s

tati

stic

)(5

.40

)(0

.76)

(7.1

7)

(2.6

7)

(1.5

2)

(7.8

3)

(4.9

9)

(0.0

6)

Inco

me±

Ho

me

val

ue

11

.00

**

1.8

38.9

9**

1.1

4**

0.9

8*

6.8

1**

10

.48

**

0.4

841.7

2

(t-s

tati

stic

)(5

.13

)(0

.69)

(7.2

5)

(2.6

9)

(1.7

3)

(7.6

7)

(4.9

4)

(0.2

7)

Inco

me

c24

6.3

1**

3.1

357.0

6**

20.4

3**

6.1

174.8

**

30

.31

**

7.8

6*

±

Liq

uid

wea

lth±

Fu

ture

wea

lth

ÿ1.7

2**

0.2

1(0

.33)

0.1

9**

(0.0

3)

0.1

40.9

2**

1.0

0**

0.3

8

(t-s

tati

stic

)(3

.06

)(0

.31)

(1.2

9)

(2.4

6)

(0.1

9)

(0.7

8)

(2.5

3)

(2.0

0)

Liq

uid

wea

lth±

Pro

per

ty(0

.16

)0

.5*

0.0

00.1

3**

(0.0

4)

0.4

4**

(0.1

2)

0.3

11.0

6

(t-s

tati

stic

)(0

.93

)(1

.66)

(0.0

1)

(3.6

0)

(1.0

2)

(3.5

7)

(0.8

3)

(0.8

3)

Liq

uid

wea

lth±

Ho

me

val

ue

(0.5

1)

0.3

70.1

10.1

4**

0.1

10.6

0**

0.0

90.6

8**

1.6

0

(t-s

tati

stic

)(1

.29

)(0

.65)

(0.6

8)

(2.8

5)

(1.2

1)

(3.2

3)

(0.3

3)

(2.0

9)

Liq

uid

wea

lth

c21

0.7

9**

2.9

42.4

317.7

7**

4.2

016.1

6**

8.0

9**

7.8

5**

±

Fu

ture

wea

lth

±P

rop

erty

1.5

6**

0.2

90.3

4ÿ0

.06

ÿ0.0

10.3

0*

ÿ1.0

5**

ÿ0.6

90.6

8

(t-s

tati

stic

)(2

.79

)(0

.42)

(1.2

9)

(0.7

2)

(0.0

8)

(1.6

6)

(2.8

3)

(1.3

7)

Fu

ture

wea

lth

±H

om

eval

ue

1.2

1*

0.1

70.4

5ÿ0

.05

0.1

40.4

6**

ÿ0.8

3*

ÿ0.3

31.2

2

(t-s

tati

stic

)(1

.79

)(0

.20)

(1.5

5)

(0.5

6)

(0.7

1)

(2.0

9)

(1.8

3)

(0.5

8)

Pro

per

ty±

Ho

me

val

ue

ÿ0.3

5ÿ0

.13

0.1

10.0

10.1

5*

0.1

70.2

20.3

60.5

4

(t-s

tati

stic

)(0

.91

)(0

.21)

(0.6

1)

(0.1

8)

(1.8

5)

(1.0

0)

(0.6

9)

(1.1

3)

Oth

erc2

8.4

7**

0.2

02.4

20.5

23.5

24.4

78.0

8**

2.8

2±

**

Sig

nif

ican

tat

5p

erce

nt

level

,*

Sig

nif

ican

tat

10

per

cent

level

.a

All

isth

esu

mo

fth

ein

com

eo

rw

ealt

hco

effi

cien

tsfo

ral

lof

the

consu

mpti

on

cate

gori

es.

Th

ec2

test

sth

ejo

int

hy

poth

esis

that

the

dif

fere

nce

sbet

wee

nth

enam

edco

effi

cien

tan

dal

lth

eoth

erco

effi

cien

tsar

eze

ro.


Tab

le4

Ex

pen

dit

ure

fun

ctio

nre

sult

s±

reg

ress

ion

stat

isti

csan

dw

ealt

hco

effi

cien

tsfo

rth

eco

nst

rain

edan

dunco

nst

rain

edsu

bsa

mple

s

Gro

ceri

esF

oo

dO

ut

Char

ity

Dues

Ente

rtai

nm

ent

Gif

tsT

ransp

ort

Vac

atio

nA

lla

All

coef

fici

ents

c24

3.9

6**

71

.66

**

22.6

219

624

**

733.3

2**

21.7

014

6.9

1**

1237.4

**

Wea

lth

coef

fici

ents

c21

9.8

8**

17

.56

**

4.5

1778.7

**

75.9

9**

5.5

727.3

1**

303.3

**

Res

ult

sfo

rth

eco

nst

rain

edsu

bsa

mp

le

R2

0.1

20

.11

0.3

30.0

30.0

30.0

20.0

20.0

2

#o

fo

ber

vati

on

s9

57

85

1834

227

92

786

312

96

Est

imat

edm

arg

inal

pro

pen

siti

esto

con

sum

e

Inco

me

13

.69

**

ÿ4.4

63.9

40.7

8ÿ3

.03

**

5.4

8**

7.2

8*

1.5

625.2

5

Liq

uid

wea

lth

ÿ1.8

64

.92

ÿ1.7

50.1

20.7

70.4

30.4

0ÿ2

.01

1.0

1

Fu

ture

wea

lth

3.1

7**

0.2

3ÿ0

.10

ÿ0.0

30.3

80.1

4ÿ0

.39

ÿ1.2

42.1

6

Pro

per

ty0

.73

0.6

10.1

3ÿ0

.11

0.2

50.3

31.0

1**

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In Table 2, the line titled `Measurement Error MA c2' contains the chi-square statistics

for a Hausman test on whether measurement error follows a first order moving average

process (the null hypothesis is that measurement error is white noise). This test consists of

comparing the estimates when the instruments are one period away (for example, using

wealth from 1973 and 1977 to instrument 1975 wealth) which are valid and most efficient

if the measurement error is white noise to those when the instruments are two periods

away (in same example, using 1971 and 1979 wealth as instruments) which are valid if

the measurement error is either white noise or follows a first order moving average

process.14 The line titled `Simultaneity c2' has the same interpretation except that the null

hypothesis is no simultaneity bias. In this case estimates using current and past values of

the wealth variables are compared to estimates that use only the past values of the wealth

variables as instruments. For both tests the null hypothesis is rejected at the 5 percent

level only for the Food Out category, and even those results do not change much when the

more robust estimator is used (i.e. the coefficients do not change much but the t-statistics

become lower). In general then, it seems safe to assume that the measurement error in the

data does not have a significant moving average component and that the effect of

simultaneity bias, if it exists, is small. The c2 tests in Table 4 will be explained below.

4.2. Tests of the behavioral life-cycle theory

The estimates for the income and the wealth variables are reported in two parts. The

first part (Table 2) consists of the coefficients and the t-statistics. Since the income and

wealth variables are divided by one-hundred before entering the regression, the

coefficients on these variables are the number of cents spending on a particular category

increases when the wealth or income variable is increased by one dollar. The second part

(Table 3) consists of tests of linear restrictions on whether various wealth and income

coefficients are equal. For example, the row labelled Ìncome±Liquid Wealth' consists of

the differences between Income and Liquid wealth coefficients (with the t-statistic for

that difference below it). The rows labelled with `c2' are chi-square statistics for the null

hypothesis that the sets of coefficients are equal. There are three sets of c2 statistics. The

first chi-square (labelled Ìncome c2') tests the null hypothesis that the coefficient on

income is equal to the coefficients of the four different wealth variables. The second set

(labelled `Liquid c2') tests the hypothesis that the coefficient on liquid wealth is equal to

the coefficients of the three remaining wealth variables. The last chi-square (labelled

Òther c2') tests whether the three remaining coefficients are equal.

In general the results from the wealth variable are more consistent with behavioral

models of consumption than with the simplest life-cycle model. Income has a large and

significantly positive effect on spending in six of the eight categories (for entertainment

the significance level is only 10 percent) even though the capitalized value of the different

income streams is included in the wealth variables (the two exceptions are for the food

out category where the coefficient is still large and positive but not statistically significant

14 Of course one could do a similar test for the presence of any measurement error by comparing the resultsfrom using instruments to the results when instruments are not used. In this case the null hypothesis of nomeasurement error is always strongly rejected.


and vacation spending which is lumpy, perhaps causing individuals to be more willing to

dip into assets to pay for it (see ahead)). The effect of receiving an extra dollar of income

is to increase spending on all the categories by almost 42 cents. On the other hand, the

wealth variables have much less effect on consumption. Of the four wealth variables,

Liquid Wealth seems to have the largest effect on consumption. It is positive and

statistically significant at the 10 percent level (or better) for six of the consumption

categories. However, its effect on consumption (even when significant) is quite small. On

the aggregate measure, a dollar increase in wealth increases consumption by less than 2

cents.

4.2.1. Test 1 (Comparing the MPC from income to the MPC from wealth)

To test the behavioral life-cycle theory against the conventional life-cycle theory a

direct comparison of the marginal propensities to consume out of different assets is

needed. If the conventional life-cycle theory holds then receiving an extra dollar of

permanent income should change consumption as much as receiving an extra amount of

wealth equal to the present value of that dollar, (i.e. the from Eq. (1)). The ratio of the

marginal propensity to consume out of permanent income to the marginal propensity to

consume out of wealth will be an estimate of that from Eq. (1). From Table 1 the

aggregated value of this ratio is 41.73/1.61�25.9 which means that a $ 1 increase in

income has as much effect on consumption as a $ 26 increase in wealth. For this ratio of

the marginal propensities to spend out of income and wealth to be consistent with a

conventional life-cycle model (i.e. Eq. (2)), a couple of average age in my sample

(husband 65, wife 62) would have to (actuarially) discount income by an interest rate of

negative 2.3 percent,15 even under the heroic assumption that all the changes in income

are permanent (if the changes in income were not permanent then the ratio should be

smaller).16 Thus the ratio of the MPC of income relative to liquid wealth appears to be too

large to be consistent with conventional life-cycle theory; it is, however, consistent with

the behavioral model.

4.2.2. Test 2 (Testing for the equality of different assets' MPC)

On the other hand, comparing liquid wealth to the other wealth variables demonstrates

that individuals are much more willing to spend out of liquid assets than they are out of

other forms of wealth. In three of the eight spending categories the difference between the

coefficient of liquid wealth and property is positive and statistically significant (when the

difference is negative, the t-statistics are always small). In the aggregate, the effect of

property on aggregate consumption is quite small (around a half a penny per dollar). This

is only one-third the size of liquid wealth's effect.

A similar relationship holds between the coefficients on house value and liquid wealth.

In fact, the coefficient on housing wealth is negative for six of the eight consumption

categories and is never statistically different from zero. This implies that changes in

15 All calculations of implied interest rates adjust for mortality probabilities. Even if the household assumedinstead that it was going to survive for 30 years for sure, the implied interest rate would still be very low (about 1percent).

16 For example, social security income changes with marital status. Thus changes in social security incomecould not be considered `permanent' for both members of the household.


housing wealth have no discernable effect on consumption at all! Thus the results for both

housing and property wealth are more consistent with the behavioral life-cycle

hypothesis, which asserts that households do not treat different types of assets as being

equivalent to each other (i.e. assets do not seem to be fungible, Eq. (5) seems to describe

reality better than Eq. (4)).

Interestingly though, the difference between liquid and future wealth is much smaller.

While the differences between the two coefficients are positive five out of the eight times,

and this (positive) difference is statistically significant three of eight times, the effect of

future wealth on aggregate consumption is around 75 percent of the effect of liquid

wealth (although the effect is concentrated on grocery spending). Thus, households seem

to be more comfortable consuming out of future wealth than out of other forms of non-

liquid wealth. One possible reason for this is that future wealth is mainly the value of

social security, which increased rapidly in this period. Perhaps an increase in one period

increased people's confidence that it would continue to increase in the future.

4.2.3. Test 3 (Testing for liquidity constraints)

A standard explanation of why consumption is sensitive to income and not to wealth is

the existence of liquidity constraints. The third test examines whether the effects of

liquidity constraints are consistent with a conventional life-cycle model or instead can be

better described by a behavioral model. According to conventional life-cycle theory, the

marginal propensity to consume should be the same for all assets except for individuals

who are liquidity constrained and cannot borrow against an illiquid asset. In that case, the

marginal propensity to consume out of the illiquid asset will be zero (Eq. (6) holds).

However, for a behavioral life-cycle individual liquidity constraints occur because of the

psychological cost of using a less liquid asset. As long as more liquid assets have not been

exhausted the propensity to consume out of the less liquid asset will be zero. Only when

the individual has to dip into that asset will consumption be sensitive to its value (Eq. (7)

holds).

To examine this issue empirically, I divided my sample into liquidity constrained and

unconstrained subsamples (defined in Section 3.1). The regression results and MPC

estimates for both subsamples are in Table 4. In the box labelled `All Coefficients c2' is a

chi-square statistic and associated probability for the hypothesis that the coefficients from

the two equations are the same. In the box labelled `Wealth Coefficients c2' is a test that

just the Income and Wealth coefficients are the same for both groups. For six of the eight

categories (Charity and Gifts are the only exceptions) both hypotheses are rejected. Thus

we can be confident that the two groups are behaving differently.

Comparing the results for the unconstrained sample to the constrained sample, the most

striking result is that illiquid forms of wealth affect consumption less for the

unconstrained subsample than they do for the constrained sample (Table 3). For almost

all the consumption categories, the propensity to consume out of any form of illiquid

wealth is smaller for the unconstrained group than it is for the constrained group. The

result of this can be seen most clearly by comparing the aggregate consumption of the

two subsamples. For every extra dollar of future wealth, aggregate consumption for the

constrained subsample increases by 2.16 cents for a $ 1.00 increase in this asset's value,

while for the unconstrained group this increase is only 0.80 cents. The contrasts are even


larger for the other two assets. For the unconstrained group, the value of the propensity to

consume out of property is one-thirteenth of the value estimated for the constrained group

(0.25 cents per dollar for the unconstrained group versus 3.26 cents of extra spending per

dollar for the constrained group). The most extreme difference is caused by changes in

housing wealth. The unconstrained group's propensity to consume out of housing is

generally negative (six of eight times) and has an aggregate value of ÿ0.59 cents! In

contrast, the constrained group's marginal propensity to consume out of housing wealth is

quite large (5.42 cents out of every dollar of appreciation). Thus the unconstrained

group's propensity to consume out of illiquid forms of wealth is significantly lower than

the constrained sample ± just the reverse of what the external liquidity constraint

hypothesis would have predicted but exactly in line with the prediction of the behavioral

life-cycle. Individuals do not appear to finance consumption out of less tempting or

illiquid assets unless their more liquid assets are exhausted. Thus liquidity constraints

seem to be internally not externally imposed.

The observed difference between the constrained and unconstrained groups' marginal

propensity to consume out of illiquid forms of wealth cannot be attributed to higher

spending patterns of the constrained group. Note that the unconstrained group's marginal

propensity to consume out of income is more than 50 percent larger (at over 40 cents on

the dollar) than the constrained group's marginal propensity to consume out of income

(about 25 cents). This is a very counter-intuitive result since it implies that the

consumption of the unconstrained tracks income more than the consumption of the

constrained group. This contradictory behavior is hard to explain with the conventional

model but may be consistent with the behavioral model. For the poorer constrained group

an extra dollar of income might have a higher chance of being spent on a good that is not

included in this study (for example, rent, non-food groceries, clothing, utilities, etc).17

However, the constrained group has already broken the mental barrier against spending

out of the illiquid assets. Therefore, their spending will be sensitive to changes in those

assets, whereas the unconstrained group's spending will not be very sensitive. Further, the

propensity to consume out of wealth may be higher for the constrained group because

these are the individuals who have been less successful at saving and so are more tempted

by their less liquid assets; in contrast the unconstrained subsample contains relatively

successful savers who may have adopted the behavioral rule of not consuming out of less

tempting forms of wealth.

A behavioral bequest motive may also help to explain the failure of the unconstrained

group to spend out of their illiquid assets. Individuals with a bequest motive may have

tried to lock in their bequest by investing it in an illiquid asset (like their house) that they

are less tempted to use for their own consumption. Thus owning a large illiquid asset may

act as a disciplinary device to insure the desired bequest occurs. Unlike a standard

bequest motive, however, this strategy implies that the size of the bequest is not neutral

with respect to which asset changes in value. A large increase in home value will be

entirely `saved' for a bequest while an equivalent rise in a more liquid asset will not.

17 As an example, note that the only good whose marginal propensity to consume out of income is higher forthe constrained group is Groceries, which is almost certainly not a luxury good.


Even though the results for both the constrained and unconstrained groups are not

consistent with models of conventional liquidity constraints they are consistent with

predictions made by the behavioral life-cycle model. Thus liquidity constraints seem not

to arise from an external market failure as much as an internal desire not to spend out of

certain types of assets unless one has to.

4.2.4. Test 4 (Testing for psychological versus financial transaction

costs)

As stated earlier, the results from the liquidity test are consistent with the existence of

financial transaction costs as well as psychological transactions costs. The testable

difference between these two theories is that if the costs of spending of an asset were only

financial then variations in asset holdings would affect the overall level spending but not

the composition of that spending. In this case the amount a conventional life-cycle

individual spends on a particular good should only depend on his total resources and the

wealth elasticity of that good. Therefore, transforming one asset into another should not

affect the split of his spending between different goods. On the other hand, Shefrin and

Thaler (1981) posit that behavioral life-cycle individuals create separate mental accounts

for the different goods they buy analogous to separate mental accounts they have for

different assets. In this case, individuals may be more willing to spend a particular asset

on one good than on another. For example, an increase in housing equity coupled with an

equivalent decrease in another asset may cause vacation spending to rise while grocery

spending falls. Observation of this type of behavior then provides direct evidence for the

behavioral life-cycle theory.

One potential problem with this strategy is that with the exception of the constrained

group, consumption is not very sensitive to changes in any type of wealth. This may

make it difficult to find much of a relationship between the values of particular assets

and the amount of spending on a good even if the behavioral life-cycle hypothesis is

true.

To test for the effect mentioned above one has to compare the ratios of the

marginal propensities to consume out of particular assets for different goods (doing

this controls for goods having different wealth elasticities ± see the discussion of Test 4

in Section 2 for the derivation). Under the conventional life-cycle hypothesis the

ratios should be equal, whereas under the behavioral life-cycle hypothesis they may not

be.

To conduct this direct test, observations that had values for more than one consumption

category were needed. In order to maximize the number of observations, only the

consumption values for 1975, 1977, and 1979 were used (for Food Out which did not

have valid data for 1975, the 1973 values were used) and 28 separate regressions were

run, in which each consumption category was paired with another one. This task was

repeated three times, once for the overall sample and then for the constrained and

unconstrained subsamples. Using the results from these paired equations, ratios of the

wealth coefficients divided by the income coefficient were constructed for each of the

categories. Then using a Wald test, the equality of these ratios between the two equations

was tested for. For example, consider consumption goods G and H with estimated

coefficients on the wealth and income variables GI, HI (for income), GL, HL (for liquid


wealth), GF, HF (for future wealth), GP, HP (for property wealth), and GH, HH (for home

wealth), the test statistic is a c2 for the joint hypothesis that

GL

GI

� HL

HI

andGP

GI

� HP

HI

andGF

GI

� HF

HI

andGH

GI

� HH

HI

andGP

GL

� HP

HL

andGF

GL

� HF

HL

andGH

GL

� HH

HL

andGF

GP

� HF

HP

andGH

GP

� HH

HP

andGH

GF

� HH

HF

The results for the entire sample were completely negative. It turns out that NONE of

the 28 c2 statistics was statistically significant at even the 10 percent level (in other words

Eq. (10) of Section 2 was never rejected). What may have occurred is that the power of

the test is quite weak. First, the number of observations in each pair of equations was

relatively low (since only a portion of the data was used). Probably more importantly,

other than the coefficients for Income and Liquid wealth the coefficients on the assets are

usually not statistically different from zero. Because the values of the different assets do

not affect consumption very much and their coefficients may just be reflecting random

noise, it is not very surprising that their ratios do not differ in a statistically significant

way.

The results change, however, when the two groups are separated. The results for the

unconstrained group are similar to the results for the combined group discussed above.

For none of the 28 different pairings can one reject the hypothesis that the ratios are the

same for both equations. Again, this is not surprising since the assets have relatively little

effect on consumption spending.

For the constrained group, however, the results are strikingly different. For eight of the

28 pairings, the hypothesis of equal ratios can be rejected (once at the 10 percent level or

better, seven times at the 5 percent level). Vacation spending was most likely to reject the

equal ratio test (four out of eight times) perhaps because vacations are more like a durable

good than the other seven. The complete list of comparisons can be found in the table

below.

As discussed earlier, constrained consumers' spending is more sensitive to changes in

assets than is the spending of unconstrained consumers. Thus this group provides a better

test of whether or not the composition of assets that individuals own affects not only the

level but also the composition of their spending. For this group, the result is a very strong

yes and so provides very strong evidence of framing.


5. Conclusion

This paper has four major results. First, spending seems to be very sensitive to changes

in income but much less sensitive to changes in wealth. Second, close examination of the

relation of wealth to consumption reveals a pattern in which individuals treat assets as not

being fungible (i.e. equivalent to each other). Third, liquidity constraints affect

consumption not as the conventional model predicts but in a manner consistent with

the existence of either financial or psychological transaction costs. The affect of these

constraints may also be evidence of a behavioral bequest motive. Finally, the amount

spent on particular goods seems to depend not only on the individual's total resources but

also on how those resources are split between different assets. Overall the patterns in the

data provide evidence in favor of the behavioral life-cycle model. Any defense of the

conventional life-cycle model will have to explain the anomalous results obtained here.

Although that may prove possible, the behavioral life-cycle model which incorporates

problems of self-control into a standard life-cycle framework, is a relatively simple

explanation of the patterns found in this data.

Acknowledgements

I would like to thank Doug Bernheim, Hersh Shefrin, Bill Sundstrom, members of the

Applied Micro Workshops at Stanford and U.C. Davis, participants at the Econometric

Society meeting on Saving in New Orleans and participants at the Russell Sage

Conference on Behavioral Theories of Savings for comments and suggestions on this

paper. I would also like to thank Clint Cummins for much computer assistance.

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